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On just about every song from her 1998 debut, “Turn the Heat Up,” Shemekia Copeland sounds like she can’t wait to get to the chorus so she can show off her blues-belting power. But she doesn’t sing like that anymore.

Today, Copeland — who plays four nights next week at Jazz Alley — sounds like she wants to tell you a story.

“When I was younger, gosh, I didn’t know what the hell I was doing,” says the Chicago-based singer, 36, by phone from New Orleans. “ I didn’t have any training, or anything, I just started singing.”

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Shemekia Copeland

Over seven albums in 17 years, mostly on Chicago’s Alligator Records, Copeland took vocal lessons and worked on nuances with producer and songwriter Oliver Wood. Throughout this year’s Grammy-nominated “Outskirts of Love,” Copeland spins clear-voiced tales of the down and out.

“I never thought I had a pretty voice, you know what I mean?” Copeland asks. “I thought I had to belt things out. I was a blues singer — that’s what I did. I didn’t think the subtlety of what I did was a good thing.”

With the help of John Hahn, her manager, and Wood, Copeland unveiled this more reflective singing style around 2009, with “Never Going Back to Memphis,” a torchy film-noir song about a criminal’s framed ex-girlfriend who replays Junior Parker in her head while cops eat fried chicken. It was a short step from there to political music, particularly 2012’s “Ain’t Gonna Be Your Tattoo,” a more straightforward ballad about domestic violence.

Copeland’s latest album, this year’s “Outskirts of Love,” is her first cycle of songs dealing exclusively with the downtrodden — homeless people in “Cardboard Box,” a date-rape victim in “Crossbone Beach,” a brush with sexual harassment in “Drivin’ Out of Nashville” and, more in line with blues conventions, the cheater in “I Feel a Sin Coming On” and the sad souls in Jessie Mae Hemphill’s “Lord, Help the Poor and Needy.”

Although Copeland is not a songwriter, she has veto power over everything Hahn and Wood present to her. She has known Hahn for almost 30 years, when he was managing her father, the late Texas blues singer Johnny “Clyde” Copeland.

“He just knows me really well — a father to me in so many ways,” she says of Hahn. “He’s very picky about (songs) he gives me. I’m very picky about what I want performed. So if I can’t jump inside of it and really become it and present it, I wouldn’t do it.”